                Patent Document 1: JP-10-246642 A (corresponding to U.S. Pat. No. 6,253,154)        Patent Document 2: JP-2000-55678 A        
A vehicular present position detection apparatus includes a car navigation system for detecting a present position of a vehicle. Conventionally, the vehicular present position detection apparatus generates a dead navigation locus (or dead reckoning trajectory) by combining a positioning receiver using a global navigation satellite system such as a GPS (Global Positioning System) with an autonomous sensor (or inertial sensor). The autonomous sensor is typified by a vehicle speed sensor or a gyroscope as an angular velocity sensor (or angular rate sensor). The vehicular present position detection apparatus collates or matches a dead navigation locus with map data to specify a position of the subject vehicle on a map.
Generally, the gyroscope detects a yaw rate of the vehicle. The vehicle speed sensor detects a travel distance. The vehicular present position detection apparatus uses the angular velocity (or yaw rate) and the travel distance to generate a motion vector of the vehicle. The vehicular present position detection apparatus integrates motion vectors to estimate a running locus (or trajectory) of the vehicle. Since the gyroscope or the vehicle speed sensor causes an error, however, a running locus may not be estimated correctly. Such errors include an offset error of the gyroscope, an angular velocity error (or yaw rate error) resulting from a gain error, and a distance coefficient error resulting from a change in a tire diameter.
For example, the technique described in Patent Document 1 estimates an  offset error and then determines a running state of the vehicle whether the vehicle turns to the right, runs straight, or turns to the left. The technique directly uses a GPS positioning result for each state to correct gains and estimate left and right gain errors. However, such technique easily causes an error due to an error in the GPS positioning result.
Patent Document 2 proposes a technique that assumes such error to be a state quantity and finds an estimated state quantity using a Kalman filter. Such technique can appropriately detect a present position of the vehicle even when the GPS position result contains an error.
As shown in a graph of FIG. 14, the gyroscope generates an output such as a voltage in proportion to an angular velocity around a predetermined axis for detection. There is a need for representing a ratio (i.e., a graph slope) of converting the gyroscope output into the angular velocity. To do this, a predetermined proportional constant (conversion gain) is used to convert the gyroscope output into the angular velocity. The converted values are integrated to find a direction variation of the vehicle.
The technique described in Patent Document 2 uses the same left and right gain characteristics for the gyroscope as shown in FIG. 14. That is, the same system is used to continuously estimate gain errors independently of whether the vehicle runs straight or turns to the left or right.
Generally, however, an actual gyroscope indicates different gain (or asymmetry gain) characteristics (different left and right sensitivities) for left and right turns as depicted by a broken line in FIG. 15. The technique of Patent Document 2 generates an angular velocity error in left and right turns and degrades the accuracy of estimating a gain error.
A Kalman filter may be used to estimate gain errors for left and right turns independently. An increase of one variable complicates a Kalman filter process.